Methods are developed for solving nonlinear equations frequently encountered at NIH, usually in the context of constrained nonlinear least squares or in the solution to nonlinear differential equations. Related problems, such as asymptotic error analysis, and the efficient treatment of sparse systems, are also considered. BIBLIOGRAPHIC REFERENCES: Winslow, R. M.; Swenberg, M.; Berger, R. L.; Shrager, R. I.; Luzzana, M.; Samaja, M.; Rossi-Bernardi, L.; Oxygen equilibrium curve of normal human blood and its evaluation by Adair's equation. J. Biol. Chem., 252, 7, 2331-2337, April 10, 1977. Lutz, R. J.; Galbraith, W. M.; Dedrick, R. L.; Shrager, R. I.; Mellett, L. B.; A model for the kinetics of distribution of actinomycin-D in the beagle dog. J. Pharm. & Exper. Ther., 200, 3, 469-478, 1977.